The councilors say money generated from their proposal would help finance substance abuse programs, so people battling addiction could receive adequate help.

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“As district city councilors, who represent neighbors feeling the impacts of substance abuse and addiction, we believe that those of us who enjoy food and drink with family and friends would not blink at the 2 percent investment,” the councilors said in a statement.

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Linehan and Baker said the revenue generated from the 2 percent tax — an estimated $20 million — would increase capacity at treatment facilities and after-care programs, leading to greater success for alcoholics and drug addicts trying to turn their lives around.

“Boston’s recovery systems need resources that this tax will provide, saving money and lives along the way,” they said. “Every time we raise a glass, let’s change the game for those who are suffering, as well as their family who share this burden.”

The public hearing is the first step in a long process before the home rule petition could become law. The plan would need the support of the City Council and Mayor Martin J. Walsh, as well as the Legislature.

Linehan and Baker teamed up last year to propose a similar measure. That proposal targeted alcohol sold at supermarkets and liquor stores. But after hearing from storeowners who felt they were being singled out, the councilors dropped the plan. The latest proposal is a more universal approach, applying to all alcohol sold in the city.

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“We all must contribute,” the councilors said in a statement.

Earlier this year, opponents of the measure said the proposed “tax on a tax” could hurt small businesses.